3x^2(x-2)(9x^2-16)(x^2+14)(3x^2+5x+2)(x^3-27)=0

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Solution for 3x^2(x-2)(9x^2-16)(x^2+14)(3x^2+5x+2)(x^3-27)=0 equation: 


Simplifying
3x2(x + -2)(9x2 + -16)(x2 + 14)(3x2 + 5x + 2)(x3 + -27) = 0

Reorder the terms:
3x2(-2 + x)(9x2 + -16)(x2 + 14)(3x2 + 5x + 2)(x3 + -27) = 0

Reorder the terms:
3x2(-2 + x)(-16 + 9x2)(x2 + 14)(3x2 + 5x + 2)(x3 + -27) = 0

Reorder the terms:
3x2(-2 + x)(-16 + 9x2)(14 + x2)(3x2 + 5x + 2)(x3 + -27) = 0

Reorder the terms:
3x2(-2 + x)(-16 + 9x2)(14 + x2)(2 + 5x + 3x2)(x3 + -27) = 0

Reorder the terms:
3x2(-2 + x)(-16 + 9x2)(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0

Multiply (-2 + x) * (-16 + 9x2)
3x2(-2(-16 + 9x2) + x(-16 + 9x2))(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0
3x2((-16 * -2 + 9x2 * -2) + x(-16 + 9x2))(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0
3x2((32 + -18x2) + x(-16 + 9x2))(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0
3x2(32 + -18x2 + (-16 * x + 9x2 * x))(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0
3x2(32 + -18x2 + (-16x + 9x3))(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0

Reorder the terms:
3x2(32 + -16x + -18x2 + 9x3)(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0
3x2(32 + -16x + -18x2 + 9x3)(14 + x2)(2 + 5x + 3x2)(-27 + x3) = 0

Multiply (32 + -16x + -18x2 + 9x3) * (14 + x2)
3x2(32(14 + x2) + -16x * (14 + x2) + -18x2 * (14 + x2) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2((14 * 32 + x2 * 32) + -16x * (14 + x2) + -18x2 * (14 + x2) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2((448 + 32x2) + -16x * (14 + x2) + -18x2 * (14 + x2) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2(448 + 32x2 + (14 * -16x + x2 * -16x) + -18x2 * (14 + x2) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2(448 + 32x2 + (-224x + -16x3) + -18x2 * (14 + x2) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2(448 + 32x2 + -224x + -16x3 + (14 * -18x2 + x2 * -18x2) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2(448 + 32x2 + -224x + -16x3 + (-252x2 + -18x4) + 9x3 * (14 + x2))(2 + 5x + 3x2)(-27 + x3) = 0
3x2(448 + 32x2 + -224x + -16x3 + -252x2 + -18x4 + (14 * 9x3 + x2 * 9x3))(2 + 5x + 3x2)(-27 + x3) = 0
3x2(448 + 32x2 + -224x + -16x3 + -252x2 + -18x4 + (126x3 + 9x5))(2 + 5x + 3x2)(-27 + x3) = 0

Reorder the terms:
3x2(448 + -224x + 32x2 + -252x2 + -16x3 + 126x3 + -18x4 + 9x5)(2 + 5x + 3x2)(-27 + x3) = 0

Combine like terms: 32x2 + -252x2 = -220x2
3x2(448 + -224x + -220x2 + -16x3 + 126x3 + -18x4 + 9x5)(2 + 5x + 3x2)(-27 + x3) = 0

Combine like terms: -16x3 + 126x3 = 110x3
3x2(448 + -224x + -220x2 + 110x3 + -18x4 + 9x5)(2 + 5x + 3x2)(-27 + x3) = 0

Multiply (448 + -224x + -220x2 + 110x3 + -18x4 + 9x5) * (2 + 5x + 3x2)
3x2(448(2 + 5x + 3x2) + -224x * (2 + 5x + 3x2) + -220x2 * (2 + 5x + 3x2) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2((2 * 448 + 5x * 448 + 3x2 * 448) + -224x * (2 + 5x + 3x2) + -220x2 * (2 + 5x + 3x2) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2((896 + 2240x + 1344x2) + -224x * (2 + 5x + 3x2) + -220x2 * (2 + 5x + 3x2) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + (2 * -224x + 5x * -224x + 3x2 * -224x) + -220x2 * (2 + 5x + 3x2) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + (-448x + -1120x2 + -672x3) + -220x2 * (2 + 5x + 3x2) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + (2 * -220x2 + 5x * -220x2 + 3x2 * -220x2) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + (-440x2 + -1100x3 + -660x4) + 110x3 * (2 + 5x + 3x2) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + -440x2 + -1100x3 + -660x4 + (2 * 110x3 + 5x * 110x3 + 3x2 * 110x3) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + -440x2 + -1100x3 + -660x4 + (220x3 + 550x4 + 330x5) + -18x4 * (2 + 5x + 3x2) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + -440x2 + -1100x3 + -660x4 + 220x3 + 550x4 + 330x5 + (2 * -18x4 + 5x * -18x4 + 3x2 * -18x4) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + -440x2 + -1100x3 + -660x4 + 220x3 + 550x4 + 330x5 + (-36x4 + -90x5 + -54x6) + 9x5 * (2 + 5x + 3x2))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + -440x2 + -1100x3 + -660x4 + 220x3 + 550x4 + 330x5 + -36x4 + -90x5 + -54x6 + (2 * 9x5 + 5x * 9x5 + 3x2 * 9x5))(-27 + x3) = 0
3x2(896 + 2240x + 1344x2 + -448x + -1120x2 + -672x3 + -440x2 + -1100x3 + -660x4 + 220x3 + 550x4 + 330x5 + -36x4 + -90x5 + -54x6 + (18x5 + 45x6 + 27x7))(-27 + x3) = 0

Reorder the terms:
3x2(896 + 2240x + -448x + 1344x2 + -1120x2 + -440x2 + -672x3 + -1100x3 + 220x3 + -660x4 + 550x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: 2240x + -448x = 1792x
3x2(896 + 1792x + 1344x2 + -1120x2 + -440x2 + -672x3 + -1100x3 + 220x3 + -660x4 + 550x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: 1344x2 + -1120x2 = 224x2
3x2(896 + 1792x + 224x2 + -440x2 + -672x3 + -1100x3 + 220x3 + -660x4 + 550x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: 224x2 + -440x2 = -216x2
3x2(896 + 1792x + -216x2 + -672x3 + -1100x3 + 220x3 + -660x4 + 550x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: -672x3 + -1100x3 = -1772x3
3x2(896 + 1792x + -216x2 + -1772x3 + 220x3 + -660x4 + 550x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: -1772x3 + 220x3 = -1552x3
3x2(896 + 1792x + -216x2 + -1552x3 + -660x4 + 550x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: -660x4 + 550x4 = -110x4
3x2(896 + 1792x + -216x2 + -1552x3 + -110x4 + -36x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: -110x4 + -36x4 = -146x4
3x2(896 + 1792x + -216x2 + -1552x3 + -146x4 + 330x5 + -90x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: 330x5 + -90x5 = 240x5
3x2(896 + 1792x + -216x2 + -1552x3 + -146x4 + 240x5 + 18x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: 240x5 + 18x5 = 258x5
3x2(896 + 1792x + -216x2 + -1552x3 + -146x4 + 258x5 + -54x6 + 45x6 + 27x7)(-27 + x3) = 0

Combine like terms: -54x6 + 45x6 = -9x6
3x2(896 + 1792x + -216x2 + -1552x3 + -146x4 + 258x5 + -9x6 + 27x7)(-27 + x3) = 0

Multiply (896 + 1792x + -216x2 + -1552x3 + -146x4 + 258x5 + -9x6 + 27x7) * (-27 + x3)
3x2(896(-27 + x3) + 1792x * (-27 + x3) + -216x2 * (-27 + x3) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2((-27 * 896 + x3 * 896) + 1792x * (-27 + x3) + -216x2 * (-27 + x3) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2((-24192 + 896x3) + 1792x * (-27 + x3) + -216x2 * (-27 + x3) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + (-27 * 1792x + x3 * 1792x) + -216x2 * (-27 + x3) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + (-48384x + 1792x4) + -216x2 * (-27 + x3) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + (-27 * -216x2 + x3 * -216x2) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + (5832x2 + -216x5) + -1552x3 * (-27 + x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + (-27 * -1552x3 + x3 * -1552x3) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + (41904x3 + -1552x6) + -146x4 * (-27 + x3) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + (-27 * -146x4 + x3 * -146x4) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + (3942x4 + -146x7) + 258x5 * (-27 + x3) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + 3942x4 + -146x7 + (-27 * 258x5 + x3 * 258x5) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + 3942x4 + -146x7 + (-6966x5 + 258x8) + -9x6 * (-27 + x3) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + 3942x4 + -146x7 + -6966x5 + 258x8 + (-27 * -9x6 + x3 * -9x6) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + 3942x4 + -146x7 + -6966x5 + 258x8 + (243x6 + -9x9) + 27x7 * (-27 + x3)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + 3942x4 + -146x7 + -6966x5 + 258x8 + 243x6 + -9x9 + (-27 * 27x7 + x3 * 27x7)) = 0
3x2(-24192 + 896x3 + -48384x + 1792x4 + 5832x2 + -216x5 + 41904x3 + -1552x6 + 3942x4 + -146x7 + -6966x5 + 258x8 + 243x6 + -9x9 + (-729x7 + 27x10)) = 0

Reorder the terms:
3x2(-24192 + -48384x + 5832x2 + 896x3 + 41904x3 + 1792x4 + 3942x4 + -216x5 + -6966x5 + -1552x6 + 243x6 + -146x7 + -729x7 + 258x8 + -9x9 + 27x10) = 0

Combine like terms: 896x3 + 41904x3 = 42800x3
3x2(-24192 + -48384x + 5832x2 + 42800x3 + 1792x4 + 3942x4 + -216x5 + -6966x5 + -1552x6 + 243x6 + -146x7 + -729x7 + 258x8 + -9x9 + 27x10) = 0

Combine like terms: 1792x4 + 3942x4 = 5734x4
3x2(-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -216x5 + -6966x5 + -1552x6 + 243x6 + -146x7 + -729x7 + 258x8 + -9x9 + 27x10) = 0

Combine like terms: -216x5 + -6966x5 = -7182x5
3x2(-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1552x6 + 243x6 + -146x7 + -729x7 + 258x8 + -9x9 + 27x10) = 0

Combine like terms: -1552x6 + 243x6 = -1309x6
3x2(-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1309x6 + -146x7 + -729x7 + 258x8 + -9x9 + 27x10) = 0

Combine like terms: -146x7 + -729x7 = -875x7
3x2(-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1309x6 + -875x7 + 258x8 + -9x9 + 27x10) = 0
(-24192 * 3x2 + -48384x * 3x2 + 5832x2 * 3x2 + 42800x3 * 3x2 + 5734x4 * 3x2 + -7182x5 * 3x2 + -1309x6 * 3x2 + -875x7 * 3x2 + 258x8 * 3x2 + -9x9 * 3x2 + 27x10 * 3x2) = 0
(-72576x2 + -145152x3 + 17496x4 + 128400x5 + 17202x6 + -21546x7 + -3927x8 + -2625x9 + 774x10 + -27x11 + 81x12) = 0

Solving
-72576x2 + -145152x3 + 17496x4 + 128400x5 + 17202x6 + -21546x7 + -3927x8 + -2625x9 + 774x10 + -27x11 + 81x12 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1309x6 + -875x7 + 258x8 + -9x9 + 27x10) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1309x6 + -875x7 + 258x8 + -9x9 + 27x10)' equal to zero and attempt to solve:

Simplifying
-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1309x6 + -875x7 + 258x8 + -9x9 + 27x10 = 0

Solving
-24192 + -48384x + 5832x2 + 42800x3 + 5734x4 + -7182x5 + -1309x6 + -875x7 + 258x8 + -9x9 + 27x10 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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